Marije Martijn

The axiomatic method, the order of concepts and the hierarchy of sciences: an introduction

This special issue of Synthese ‘The Classical Model of Science II: The axiomatic method, the order of concepts and the hierarchy of sciences’ follows up on the previous ‘The ClassicalModel of Science I: Amillennia-oldmodel of scientific rationality’. Both issues centre on the role, the significance and the impact of the axiomatic ideal of scientific knowledge in the history of philosophy. The first issue focuses on the relation between axiomatics and a number of issues in the development of logic, mathematics, and methodology and philosophy of science in Aristotle, Proclus, the seventeenth century, Kant, Bolzano, Frege and Leśniewski. The papers collected in this second issue on the one hand continue to investigate that relation in Kant and Bolzano, stretching it further on to our days, via mathematicians such as Schroder, Dedekind, and Birkhoff, and on the other hand they extend that investigation to related and current issues concerning the empirical sciences, in a systematic evaluation of modern (formal) axiomatic conceptions of science. The contributions in both issues take their cue from the axiomatic ideal in question as captured in the ‘Classical Model (or Ideal) of Science’ (de Jong and Betti 2008):

Proclus on the order of philosophy of nature

In this paper I show that Proclus is an adherent of the Classical Model of Science as set out elsewhere in this issue (de Jong and Betti 2008), and that he adjusts certain conditions of the Model to his Neoplatonic epistemology and metaphysics. In order to show this, I develop a case study concerning philosophy of nature, which, despite its unstable subject matter, Proclus considers to be a science. To give this science a firm foundation Proclus distills from Plato’s Timaeus the basic concepts Being and Becoming and a number of basic propositions, among others the quasi-definitions of the basic concepts. He subsequently explains the use of these quasi-definitions, that are actually epistemic guides, in such a way that he obtains a connection between a rational and an empirical approach to the natural world. A crucial task in establishing the connection is performed by the faculty of doxa and by geometrical conversion. The result is that Proclus secures a universal, necessary and known foundation for all of philosophy of nature.

Why Beauty is Truth in all we know: Aesthetics and mimesis in Neoplatonic science

The question addressed in this programmatic paper, which connects to ongoing discussions in philosophy of science, is how beauty figures in the scientific practice according to Proclus. In order to answer that question, Neoplatonic aesthetics, philosophy of ἐπιστήμη, and philosophy of language are brought together. I present an overview of the properties associated with beauty, the nature of aesthetic experience, Proclus’ ideal of scientific knowledge, his notion of truth, and the metaphysical background of the expression of scientific knowledge. From an elaboration of these issues using Proclus’ views of the beauty of mathematics as a case-study, it becomes clear that the beauty of ἐπιστήμη lies especially in aspects of its reasoning, through which a connection is established between an ἐπιστήμη and transcendent reality. Beauty is shown to be both a criterion of the truth of scientific proofs and a tool in the reversion of the human soul to transcendent Being.

Dissertationes Batavae: Martijn, M. 2008. Proclus on Nature. Philosophy of Nature and Its Methods in

One of the hardest questions to answer for a (Neo)platonist is to what extent and how the changing and unreliable world of sense perception can itself be an object of scientific knowledge. My dissertation is a study of the answer given to that question by the Neoplatonist Proclus (Athens, 411-485) in his Commentary on Plato’s Timaeus. I present a new explanation of Proclus’ concept of nature and show that philosophy of nature consists of several related subdisciplines matching the ontological stratification of nature. Moreover, I demonstrate that for Proclus philosophy of nature is a science, albeit a hypothetical one, which takes geometry as its methodological paradigm. I also offer an explanation of Proclus’ view of what is later called the mathematization of physics, i.e. the role of the substance of mathematics, as opposed to its method, in explaining the natural world. Finally, I discuss Proclus’ views of the discourse of philosophy of nature and its iconic character.